JEE

You have a chance to get admission in NITS like NIT-Jaipur, Nagpur, Surat, Warangal, Durgapur, etc. for CSE.
Best of luck.

Drop is not necessary step for IITs. Many IITians haven't taken any step. If your focus on your goal is clear then you can also clear IIT JEE without drop.
Your concepts must be clear whether you take a drop or not.

In which state are you looking for?

First of all, you should focus on NCERT books. For additional, you can go for HC Verma in physics, for chemistry, GRB publication's books are good and for practicing numerical, you can refer Arihant books but make sure that you should not have excess study material.

Class 10th board exams are Iron GATE for you, so you can have to give proper attention to board exams. When you are free from it then you can clear your basic concepts of class 10th and the main topic comes in JEE belongs to class 11th 12th NCERT syllabus.

Yes, JEE Mains exams do have negative marks. In JEE Mains examination, for every correct answer, you will be awarded 4 marks and for a wrong answer, you will be given -1.
In JEE Advanced, there are different types of questions like assertion reason, subjective, objective, etc., and there are particular marks for each one. There are negative marks for that too.
All the best.

Hello Radhika!
BMS college of architecture, Bangalore provides admission for B.Arch only through NATA score. It does not accept jee mains paper 2 scores.
For further details, refer the following link:
http://www.bmsce.in
All the best!

You can go to some of the top private colleges accepting JEE Mains and board percentage. There you can also get scholarships up to 100% (maybe).